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The answer is: Instantaneous Acceleration.

Q: The rate at which velocity is changing at a given instant is described by?

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Instantaneous velocity is the rate at which an object is moving in a uniform direction, distance per unit time, at any given instant in time. instantaneous acceleration is the rate at which an object's velocity is changing at any given instant in time

velocity is your answer.

speed if no direction is needed velocity if direction is needed

a=dv/dt=d/dt(dx/dt)=d^2x/dt^2Is the rate of a tangent to the slope of a graph signifying velocity versus time. It is a snapshot of acceleration at a precise moment in time based on the relative changes in velocity over time. It is the limit of acceleration for any given point within the displacement vector.Instantaneous acceleration is how fast a velocity is changing at a specific instant.

Remember Newton's 2nd Law of Universal Dynamics. Force is directly proportional to the change in momentum(acceleration) . So a given force applied to a mass will change its velocity. Remember velocity is speed ( a scalar quantity) in a given direction. So an object moving at constant speed , but changing its direction ( going round in a circle /ellipse) is accelerating; its velocity is changing.

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Instantaneous velocity is the rate at which an object is moving in a uniform direction, distance per unit time, at any given instant in time. instantaneous acceleration is the rate at which an object's velocity is changing at any given instant in time

rate of motion is speed or velocity

velocity is your answer.

The speed of something in a given direction.

it can be calculated at a particular instant as it is total displacement in given time

speed if no direction is needed velocity if direction is needed

Yes. Velocity is rate (or speed) in a given direction. If you change your direction but not your rate (or speed) then you have changed your velocity without changing speed.

This is difficult. We are not told what it is we are to calculate. We are not told how the velocity is changing (which it does, implied by the word "initial"). Suggest re-writing the question.

a=dv/dt=d/dt(dx/dt)=d^2x/dt^2Is the rate of a tangent to the slope of a graph signifying velocity versus time. It is a snapshot of acceleration at a precise moment in time based on the relative changes in velocity over time. It is the limit of acceleration for any given point within the displacement vector.Instantaneous acceleration is how fast a velocity is changing at a specific instant.

this time is basically the instant when an object has a particular velocity(instantaneous velocity). so on the graph draw a line from the particular value of the velocity and then draw a vertical line on time axis to find the time for that velocity.

Remember Newton's 2nd Law of Universal Dynamics. Force is directly proportional to the change in momentum(acceleration) . So a given force applied to a mass will change its velocity. Remember velocity is speed ( a scalar quantity) in a given direction. So an object moving at constant speed , but changing its direction ( going round in a circle /ellipse) is accelerating; its velocity is changing.

Velocity is Speed in a given direction. Moving at constant velocity is equivalent to say moving with a constant speed in a specified direction. So, moving at constant velocity implicitly means moving with constant speed.